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- W3099042911 abstract "We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems: * We provide an algorithm for testing whether a hypergraph has cutwidth at most k that runs in linear time for constant k. In terms of parameterized complexity theory, the problem is fixed-parameter linear parameterized by k. * We show that it is not expressible in monadic second-order logic whether a hypergraph has bounded (fractional, generalized) hypertree width. The proof leads us to conjecture that, in terms of parameterized complexity theory, these problems are W[1]-hard parameterized by the incidence treewidth (the treewidth of the incidence graph). Thus, in the form of the Myhill-Nerode theorem for hypergraphs, we obtain a method to derive linear-time algorithms and to obtain indicators for intractability for hypergraph problems parameterized by incidence treewidth. In an appendix, we point out an error and a fix to the proof of the Myhill-Nerode theorem for graphs in Downey and Fellow's book on parameterized complexity." @default.
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- W3099042911 date "2015-02-26" @default.
- W3099042911 modified "2023-10-02" @default.
- W3099042911 title "Myhill–Nerode Methods for Hypergraphs" @default.
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- W3099042911 doi "https://doi.org/10.1007/s00453-015-9977-x" @default.
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